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A semi-analytical approach to Canary swaptions in HJM one-factor model


  • Henrard Marc

    (Bank for International Settlements)


Leveraging the explicit formula for European swaptions and coupon-bond options in HJM one-factor model, we develop a semi-explicit formula for 2-Bermudan options (also called Canary options). We first extend the European swaption formula to future times. We are able to reduce the valuation of a 2-Bermudan swaption to a single numerical integration at the first expiry date. In that integration the most complex part of the valuation of the embedded European swaptions has been simplified in such a way that it has to be performed only once and not for every point.

Suggested Citation

  • Henrard Marc, 2003. "A semi-analytical approach to Canary swaptions in HJM one-factor model," Finance 0310008, EconWPA, revised 25 Nov 2004.
  • Handle: RePEc:wpa:wuwpfi:0310008
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    References listed on IDEAS

    1. Santa-Clara, Pedro & Sornette, Didier, 2001. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 149-185.
    2. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258.
    3. John M. Mulvey & Stavros A. Zenios, 1994. "Capturing the Correlations of Fixed-income Instruments," Management Science, INFORMS, vol. 40(10), pages 1329-1342, October.
    4. Andrea Beltratti & Andrea Consiglio & Stavros Zenios, 1999. "Scenario modeling for the management ofinternational bond portfolios," Annals of Operations Research, Springer, vol. 85(0), pages 227-247, January.
    5. Dupacova, Jitka & Bertocchi, Marida, 2001. "From data to model and back to data: A bond portfolio management problem," European Journal of Operational Research, Elsevier, vol. 134(2), pages 261-278, October.
    6. Heaney, W John & Cheng, Pao L, 1984. " Continuous Maturity Diversification of Default-Free Bond Portfolios and a Generalization of Efficient Diversification," Journal of Finance, American Finance Association, vol. 39(4), pages 1101-1117, September.
    7. Goldstein, Robert S, 2000. "The Term Structure of Interest Rates as a Random Field," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 365-384.
    8. Zenios, Stavros A. & Holmer, Martin R. & McKendall, Raymond & Vassiadou-Zeniou, Christiana, 1998. "Dynamic models for fixed-income portfolio management under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 22(10), pages 1517-1541, August.
    9. Golub, Bennett & Holmer, Martin & McKendall, Raymond & Pohlman, Lawrence & Zenios, Stavros A., 1995. "A stochastic programming model for money management," European Journal of Operational Research, Elsevier, vol. 85(2), pages 282-296, September.
    10. D. P. Kennedy, 1997. "Characterizing Gaussian Models of the Term Structure of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 107-118.
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    Cited by:

    1. Marc Henrard, 2005. "Inflation bond option pricing in Jarrow-Yildirim model," Finance 0510027, EconWPA.

    More about this item


    Bermudan option; swaption; bond option; HJM model; one-factor model; explicit formula; numerical integration.;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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